How the APR Calculator Works
The interest rate in a loan offer is not the full cost of the loan. Most loans also have fees at the start, such as an origination fee or an application fee. APR stands for annual percentage rate. It is the yearly rate that includes those fees, so it shows what the loan really costs. The APR Calculator finds it from the loan amount, the stated rate, the term and the fees.
What you enter
- Loan amount: the amount you borrow and repay.
- Stated interest rate: the rate in the offer, before fees.
- Loan term: the number of months you have to repay.
- Upfront fees: the fees you pay at the start, or that are taken out of the loan.
How the APR is worked out
First the calculator finds the monthly payment, from the loan amount and the stated rate. Here r is the monthly rate (the stated rate divided by 12) and n is the number of months:
payment = loan x r / (1 - (1 + r)^-n)
You repay that payment on the full loan, but you only receive the loan minus the fees. So the calculator looks for the monthly rate at which the payments are worth exactly what you received:
loan - fees = payment x (1 - (1 + rate)^-n) / rate APR = rate x 12
There is no simple formula for this rate, so the calculator finds it by trial and refinement, which always settles on an answer, even with a 0% loan.
A worked example
You borrow $10,000 for 36 months at a stated rate of 6.5%, and the fees are $300.
| Result | Amount |
|---|---|
| Monthly payment | $306.49 |
| Money you actually receive ($10,000 - $300) | $9,700.00 |
| Total of the payments | $11,033.64 |
| Total interest | $1,033.64 |
| Interest plus fees | $1,333.64 |
| Stated rate | 6.500% |
| Effective APR | 8.563% |
The fees add 2.063 percentage points. You pay interest on $10,000, but you only get $9,700 to use.
Chart: stated rate and APR
Stated rate ███████████████████████████████████ 6.500% APR ██████████████████████████████████████████████ 8.563%
How the fees change the APR
The same loan, with different fees:
| Fees | Amount | APR |
|---|---|---|
| None | $0 | 6.500% |
| 1% of the loan | $100 | 7.178% |
| 2% of the loan | $200 | 7.866% |
| 3% of the loan | $300 | 8.563% |
| 5% of the loan | $500 | 9.989% |
The term matters too
A fee is a fixed cost, so on a short loan it is spread over fewer months and it hurts more. The same $10,000 loan at 6.5% with $300 of fees:
| Term | Monthly payment | APR |
|---|---|---|
| 12 months | $862.96 | 12.249% |
| 24 months | $445.46 | 9.521% |
| 36 months | $306.49 | 8.563% |
| 60 months | $195.66 | 7.780% |
| 84 months | $148.49 | 7.440% |
If you plan to pay a loan off early, the fees cost you even more, because they are spread over fewer months than the APR assumes.
Tips
- Compare loans by APR, not by the stated rate. A loan with a lower rate but big fees can cost more.
- Ask what the fees are for, and whether they can be lowered or removed.
- Look at the total cost too. A longer loan can have a lower APR but costs more in total interest.
- Check for a penalty for paying early, if you might pay the loan off sooner.
What this calculator does not include
- Loans with a rate that changes, or with interest-only periods.
- Fees that are paid during the loan, such as yearly or monthly fees. Add them to the upfront fees for a rough figure.
- The exact rules a lender uses. In some places, lenders must leave out some kinds of fees, so an official APR may differ a little from this one.
This tool gives an estimate for general information only. It is not financial advice. Your loan agreement sets the real rate, fees and payment.